Manifold isometry between representations and behavior

Neural network activation and behavior manifolds maintain geometric correspondence, enabling intervention optimization across language models and vision tasks.

5 members. Each node is clickable.

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Drawn from 3 sources

The papers/notes whose extracted claims & findings make up this cluster.

Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior3 members
2026-05-14_phil-trans-A-goodfire-aboutblank-impact.md1 member
Steering Along Manifolds to Control Neural Networks1 member

Bridges (2)

Other communities that share members with this one — cross-cutting threads or papers that sit at the seam between two themes.

Findings (3)

Optimizing interventions in activation space to produce paths along M_y recovers activation trajectories that trace the curvature of M_h.Demonstrates bidirectional causal link: behavior manifold geometry can be recovered by optimizing in representation space.
Interventions along activation manifold M_h yield behavioral trajectories following behavior manifold M_y, and vice versa — bidirectional relationship demonstrated across language models and video world models.Central empirical result showing causal coupling between representation and behavior geometry across multiple substrates and modalities.
manifold geometry principles extend to months, letters, ages, and in-context learning tasks across modalitiesEvidence that the weekday cyclic structure is not anomalous but reflects broader principle of concept geometry.

Claims (2)

There is a bidirectional relationship between the geometry of representation and behavior across tasks and modalities.Author’s interpretive claim that the shared geometry is general and robust.
Activation manifolds and behavior manifolds are approximately isometric across cyclic and sequential concepts.